In mathematics, the bicyclic semigroup is an algebraic object important for the structure theory of semigroups. Although it is in fact a monoid, it is usually referred to as simply a semigroup. It is perhaps most easily understood as the syntactic monoid describing the Dyck language of balanced pairs of parentheses. Thus, it finds common applications in combinatorics, such as describing binary trees and associative algebras.
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In mathematics, the bicyclicsemigroup is an algebraic object important for the structure theory of semigroups. Although it is in fact a monoid, it is...
finite-state machine (FSM). The bicyclicsemigroup is in fact a monoid, which can be described as the free semigroup on two generators p and q, under...
meant by a regular band. The bicyclicsemigroup is regular. Any full transformation semigroup is regular. A Rees matrix semigroup is regular. The homomorphic...
semigroup S. Partial bijections on a set X form an inverse semigroup under composition. Every group is an inverse semigroup. The bicyclicsemigroup is...
mathematics, a semigroup is a nonempty set together with an associative binary operation. A special class of semigroups is a class of semigroups satisfying...
a finite set of generators is compact. The bicyclic monoid is not compact. The class of compact semigroups is closed under taking subsemigroups and finite...
presentation of a monoid (or a presentation of a semigroup) is a description of a monoid (or a semigroup) in terms of a set Σ of generators and a set of...
. The syntactic monoid of the Dyck language is isomorphic to the bicyclicsemigroup by virtue of the properties of Cl ( [ ) {\displaystyle \operatorname...
with addition form a monoid, the identity element being 0. Monoids are semigroups with identity. Such algebraic structures occur in several branches of...
minimal automaton has 4 states and the syntactic monoid has 15 elements. The bicyclic monoid is the syntactic monoid of the Dyck language (the language of balanced...